The Reserves That Didn't Match the Risk
A small life insurer writes a block of 10-year renewable term policies. It prices the block assuming a 2% annual lapse rate and a flat mortality assumption of 0.3% per annum across all ages. In fact, lapses run at 12% in year one and 8% thereafter, and mortality is heavily age-skewed: 0.1% for ages 30-45 and 1.2% for ages 55-65. The block is now in its third year. The insurer's reserves were set using the original assumptions. The actuary reports that the reserve is materially understated. The insurer's solvency ratio is 1.4x, against a regulatory minimum of 1.5x. The insurer asks whether it can simply increase premiums on renewal to restore the ratio.
1. Explain why the reserve is understated, identifying the effect of each assumption error on the reserve.
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Two assumption errors pull in opposite directions on some measures but both hurt the reserve in this case.
1. Lapse rate. Actual lapses (12% year one, 8% thereafter) are far higher than the assumed 2%. In a term product, higher lapses usually reduce the number of policies in force and therefore reduce the total reserve - but they also remove the healthier, lower-risk lives, leaving an adverse selection effect. The policies that persist are disproportionately those where the insured expects to claim, or where the insured has become uninsurable elsewhere and so will not lapse. The result is that the remaining block has higher mortality than the original pricing assumed. The reserve, set on the original 2% lapse assumption, does not reflect this anti-selective persistency.
2. Mortality. The flat 0.3% assumption is wrong in both directions. For ages 30-45 actual mortality (0.1%) is lower than assumed - that part of the block is over-reserved. For ages 55-65 actual mortality (1.2%) is four times the assumed rate - that part is severely under-reserved. Because the block is ageing, the 55-65 cohort grows each year, so the under-reserving dominates over time. A flat assumption across ages is structurally wrong for a term product.
3. Interaction. The two errors compound. High lapses concentrate the block in the older, higher-mortality ages, exactly where the mortality assumption is most wrong. The reserve is therefore understated by more than either error alone would suggest.
4. The reserve basis itself. Reserves should reflect the insurer's best estimate of future cash flows plus a risk margin. Using stale pricing assumptions as reserving assumptions is a category error: pricing assumptions include profit margins and are set at policy inception, whereas reserving assumptions must be current and prudent. The actuary is right that the reserve is materially understated.
2. Can the insurer raise renewal premiums to restore its solvency ratio? Analyse the constraints, and set out what the insurer should actually do.
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Raising renewal premiums is not a viable primary remedy, for several reasons.
1. Contractual constraints. In a 10-year renewable term policy, the insurer can only re-rate at the renewal date, and only if the policy terms permit it. Many term contracts guarantee premiums for the term or guarantee maximum renewal rates. If the contract fixes the premium, the insurer cannot unilaterally increase it mid-term. Even at renewal, a large increase invites lapses - and given the anti-selective lapse pattern already observed, the healthiest lives will leave first, worsening the mortality profile of those who stay. This is the classic death spiral.
2. Regulatory constraints. A solvency ratio of 1.4x against a 1.5x minimum is a breach. The regulator will require a remediation plan, and will scrutinise any premium increase that looks like an attempt to plug a capital hole through policyholder charges. Premium increases that are not actuarially justified by the risk of the individual policy may be treated as unfair.
3. Timing. The reserve deficiency exists now. Premium increases at renewal take years to flow through and cannot restore the ratio in the short term.
What the insurer should do:
- Recalculate reserves immediately on a current, best-estimate basis with an appropriate risk margin, and report the restated position to the regulator.
- Inject capital (from shareholders or a subordinated debt issue) to restore the ratio above 1.5x. This is the only measure that fixes the ratio now.
- Reinsure part of the block, particularly the 55-65 cohort, to reduce net exposure.
- Review renewal pricing prospectively, within contractual limits, and accept that some lapse is inevitable.
- Fix the assumption-setting process: age-banded mortality, experience-based lapse assumptions, and a regular assumption review cycle with board oversight.
- Consider closing the block to new business if the experience cannot be brought under control.
The core lesson: reserves are a balance-sheet problem and must be fixed on the balance sheet. Premium increases are a pricing tool, not a capital tool, and using them as one usually makes the underlying problem worse.